source stringclasses 6 values | subject stringclasses 26 values | question stringlengths 1 1.14k | options listlengths 3 5 | rationale stringlengths 0 22.5k β | correct stringclasses 9 values |
|---|---|---|---|---|---|
deepmind/aqua_rat | Maths-Algebra | The integer n is formed by writing the integers 1 through 333 in order as shown below.
n=123456789101112.......331332333
counting from the left, what is the 333rd digit of n? | [
"A)0",
"B)1",
"C)3",
"D)7",
"E)8"
] | the other way you can approach this is:
add zeroes as follows:
123456789....
make a pair of 3 by making each number a 3 digit number
000
001
002
003
004
005
006
007
008
009
010.... and so on
....by doing this we can make that every other 30th digit will be a 9
and for doing this we are adding 1*3+2*9+1*90=112 zeroes...therefore 333rd digit now will be 333+111=444 th digit
now 30*15=450....therefore 450th digit will be 9
and 15 th series will be of 141,142....149
so ........147148149.....in this 9 is the 450th digit therefore 444 th will be 7
hence the answer is 7 answer is D | D |
deepmind/aqua_rat | Maths-Algebra | Four friends, Peter, John, Quincy, and Andrew, are pooling their money to buy a $1600 item. Peter has twice as much money as John. Quincy has $40 more than Peter. Andrew has 10% more than Quincy. If they put all their money together and spend the $1600, they will have $14 left. How much money does Peter have? | [
"A)$400",
"B)$560",
"C)$425",
"D)$380",
"E)$455"
] | P= 2J ; Q= P+40 ; A= 1.1(Q)
P+J+Q+R-1600=14
P+0.5P+P+40+1.1(P+40) = 1614
P+0.5P+P+40+1.1P+44=1614
P+0.5P+P+1.1P+84=1614
P+0.5P+P+1.1P=1530
3.6P=1530
P=425
Answer:C | C |
deepmind/aqua_rat | Maths-Algebra | Health insurance Plan P requires the insured person to pay $600 but then the insurance pays 80% of the cost over $600. Plan Q requires the insured to pay the initial $400, but then pays 60% of the cost over $400. Which of the following is a cost level for which both insurance plans pay out the same amount? | [
"A)$1000",
"B)$1100",
"C)$1200",
"D)$1300",
"E)$1400"
] | 0.8(x-600)=0.6(x-400)
0.2x=480-240
x=1200
The answer is C. | C |
deepmind/aqua_rat | Maths-Algebra | Calculate the percentage gain if a trader bought a bicycle for Rs.440 and sold it for Rs.610? | [
"A)38.64%",
"B)39.64%",
"C)31.64%",
"D)35.64%",
"E)34.64%"
] | C.P. = 440
S.P. = 610
Gain = 610-440 ---- 170
% Gain => 170/440*100 => 38.64%
Answer:A | A |
deepmind/aqua_rat | Maths-Algebra | A ladder 22 feet long is leaning against a wall that is perpendicular to level ground. The bottom of the ladder is 7 feet from the base of the wall. If the top of the ladder slips down 3 feet, how many feet will the bottom of the ladder slip? | [
"A)12.86",
"B)15",
"C)18",
"D)19",
"E)25"
] | 22^2-7^2=435
it means that the height is equal to 20.85.
since the top of the ladder slips down 4 feet, then the height of the wall =20.85-3=17.85
the bottom =sqrt(22^2-17.85^2)=sqrt(484-318.62)=12.86
ans is A | A |
deepmind/aqua_rat | Maths-Algebra | A circular mat with diameter 14 inches is placed on a square tabletop, each of whose sides is 24 inches long. Which of the following is closest to the fraction of the tabletop covered by the mat? | [
"A)5/12",
"B)2/5",
"C)1/5",
"D)3/4",
"E)5/6"
] | SO we are looking for the area of the cloth over the area of the table
Area of the Cloth = (pi)(r)^2 which is about (3)(7)(7)
Area of the Table = (24)(24)
So the quick way to estimate is looking at the fraction like this: (3/24)(41/24)
I hope this is easy to follow, so with some simplification i get (1/8)(12/7) =3/14= (1/5) Answer is C | C |
deepmind/aqua_rat | Maths-Algebra | Which part of an atom has no electrical charge? | [
"A)q1",
"B)22",
"C)72",
"D)27",
"E)28"
] | Answer: Option B | B |
deepmind/aqua_rat | Maths-Algebra | The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ? | [
"A)Rs. 2400",
"B)Rs. 2200",
"C)Rs. 2300",
"D)Rs. 2500",
"E)Rs. 2600"
] | Let the price of a saree and a shirt be Rs. x and Rs. y respectively.
Then, 2x + 4y = 1600 .... (i)
and x + 6y = 1600 .... (ii)
Divide equation (i) by 2, we get the below equation.
=> x + 2y = 800. --- (iii)
Now subtract (iii) from (ii)
x + 6y = 1600 (-)
x + 2y = 800
----------------
4y = 800
----------------
Therefore, y = 200.
Now apply value of y in (iii)
=> x + 2 x 200 = 800
=> x + 400 = 800
Therefore x = 400
Solving (i) and (ii) we get x = 400, y = 200.
Cost of 12 shirts = Rs. (12 x 200) = Rs. 2400.
A | A |
deepmind/aqua_rat | Maths-Algebra | A company sells two products, L and M. Last year, seventy percent of the units sold were product L, and the price of product L was 25 percent greater than the price of product M. Approximately what percent of the total revenue the company received last year was from the sale of product L? | [
"A)15%",
"B)25%",
"C)35%",
"D)65%",
"E)74%"
] | Percentage of total units that is product L = 70 %
Price of product L = 25 percent greater than price of product M.
Now , we can consider this as a weighted average scenario .
If the price of both the products L and M was equal , then contribution of product L to total sales would be = 70%
But since , price of product L is greater than M , then contribution of product L to total sales will be greater than 70%
The only option is 74%
Answer E | E |
deepmind/aqua_rat | Maths-Algebra | Three numbers are in the ratio 1 : 2 : 3 and their H.C.F is 5. The numbers are | [
"A)12, 24, 30",
"B)12, 24, 38",
"C)12, 24, 362",
"D)5, 10, 15",
"E)12, 24, 321"
] | Explanation:
Let the required numbers be x, 2x, 3x. Then, their H.C.F =x. so, x= 5
\inline \fn_jvn \therefore The numbers are 5, 10, 15
Answer: D) 5, 10, 15 | D |
deepmind/aqua_rat | Maths-Algebra | In how many no. between 10 and 40 exactly Two of the digits is 4? | [
"A)10",
"B)15",
"C)35",
"D)1",
"E)45"
] | It's simple can be solved by elimination of answer choices.
Option B and C are too large, not possible. Even AE are large to have correct choice.
Ans : D | D |
deepmind/aqua_rat | Maths-Algebra | From given equation find the value of x: 2xΒ² + 9x β 5 | [
"A)1",
"B)1/2",
"C)1/3",
"D)2/3",
"E)2/5"
] | That quadratic is factored as follows:
2xΒ² + 9x β 5 = (2x β 1)(x + 5).
Lesson 17.
Now, it is easy to see that the second factor will be 0 when x = β5.
As for the value of x that will make
2x β 1 = 0,
we must solve that little equation. (Lesson 9.)
We have:
2x = 1
x = 1
2
The solutions are:
x = 1/2 or β5
B | B |
deepmind/aqua_rat | Maths-Algebra | A garrison of 2000 men has provisions for 40 days. At the end of 20 days, a reinforcement arrives, and it is now found that the provisions will last only for 10 days more. What is the reinforcement? | [
"A)1888",
"B)2766",
"C)2999",
"D)2000",
"E)1712"
] | 2000 ---- 40
2000 ---- 20
x ----- 10
x*10 = 2000*20
x = 4000
2000
-------
2000
Answer: D | D |
deepmind/aqua_rat | Maths-Algebra | What is the total number of positive integers that are less than 200 and that have no positive factor in common with 200 other than 1? | [
"A)60",
"B)70",
"C)80",
"D)90",
"E)100"
] | Since 200=2^3*5^2 then a number can not have 2 and/or 5 as a factor.
The odd numbers do not have 2 as a factor and there are 100 odd numbers from 1 to 200.
We then need to eliminate the 20 numbers that end with 5, that is 5, 15, 25,...,195.
There are a total of 100 - 20 = 80 such numbers between 1 and 200.
The answer is C. | C |
deepmind/aqua_rat | Maths-Algebra | P and Q are both positive integers. When P is divided by Q, the remainder is some positive integer D, and when P is divided by (Q + 4), the remainder is also D. If P/Q = 1020.75 and P/(Q + 4) = 816.6, then which of the following gives the correct set of {D, Q}? | [
"A){6, 12}",
"B){6, 15}",
"C){12, 16}",
"D){9, 15}",
"E){15, 24}"
] | p/q= d=p/q+4
d= .75 q
d= .6(q+4)
we get d = 12 and q = 16. Answer = C. | C |
deepmind/aqua_rat | Maths-Algebra | A bus from city M is traveling to city N at a constant speed while another bus is making the same journey in the opposite direction at the same constant speed. They meet in point P after driving for 2 hours. The following day the buses do the return trip at the same constant speed. One bus is delayed 24 minutes and the other leaves 36 minutes earlier. If they meet 24 miles from point P, what is the distance T between the two cities? | [
"A)48",
"B)72",
"C)96",
"D)120",
"E)192"
] | Hmmm I did this question a while ago and got it wrong so trying again
Rate x time = distance.
For the initial trip lets the distance T to the midpoint be represented by P.
EQN1: R x 2 = P
For the second trip we know one bus left late and one left early. Together this is just a tricky way of saying one bus left an hour after the other. We know the total trip takes 4 hours (since getting to P is 2 hours). The second trip can be represented by:
Since the trip takes 4 hours if a bus leaves one hour early, the reminaining 3 hours are split between the two buses, ie. 1 + 3/2 = 2.5
EQN2: R x 2.5 = P + 24
EQN2-EQN1 : 0.5R=24
R=48
So the distance is rate x time = 48 x 4 = 192.
ANS = E | E |
deepmind/aqua_rat | Maths-Algebra | The H.C.F. of two numbers is 12 and their L.C.M. is 520. If one of the numbers is 480, then the other is: | [
"A)13",
"B)18",
"C)21",
"D)24",
"E)38"
] | Other number = (12 x 520)/480 = 13.
ANSWER :A | A |
deepmind/aqua_rat | Maths-Algebra | Rahul went to a shop and bought things worth Rs. 25, out of which 36 Paise went on sales tax on taxable purchases. If the tax rate was 6%, then what was the cost of the tax free items? | [
"A)19",
"B)18.7",
"C)19.9",
"D)21.7",
"E)22.8"
] | Total cost of the items he purchased = Rs.25
Given that out of this Rs.25, 36 Paise is given as tax
=> Total tax incurred = 36 Paise = Rs.36/100
Let the cost of the tax free items = x
Given that tax rate = 6%
β΄ (25β36/100βx)6/100 = 36/100
β 6(25 β0.36 βx) = 36
β (25 β 0.36 β x) = 6
β x = 25 β 0.36 β 6 = 18.7
B) | B |
deepmind/aqua_rat | Maths-Algebra | In a certain year, the population of a certain town was 9000. If in the next year the population of males increases by 3% and that of the females by 8% and the total population increases to 9600, then what was the ratio of population of males and females in that given year? | [
"A)4 : 11",
"B)5 : 4",
"C)2 : 3",
"D)Data inadequate",
"E)None of these"
] | Let the population of males = x; then the population of females = 9000 β x
Now, 3% of x + 8% of (9000 β x)
= (9600 β 9000 ) = 600
or 0.03x + 720 β 0.08x = 600
or 720 β 600 = 0.08x β 0.03x
or, 120 = 0.05x
x = 2400
Reqd ratio of population of males and females
2400/9000β2400=2400/6600=4:11
Answer A | A |
deepmind/aqua_rat | Maths-Algebra | Find 3486/189 | [
"A)18.44",
"B)18.48",
"C)18.42",
"D)18.49",
"E)18.41"
] | First we make the denominator 200. i.e., we are introducing an error of 11 which is 11189=11711189=117 th of the denominator.
Now 3486200=17.433486200=17.43
But this answer is less than actual answer. So we have to increase it by 1/17th part of it.
117Γ17.43β1117Γ17.43β1
So final answer = 17.43 + 1 = 18.43
Actual answer = 18.44
Answer:A | A |
deepmind/aqua_rat | Maths-Algebra | If you write down all the numbers from 1 to 50, then how many times do you write 3 ? | [
"A)A)11",
"B)B)15",
"C)C)20",
"D)D)21",
"E)E)22"
] | Explanation:
Explanation:
Clearly, from 1 to 50, there are ten numbers with 3 as the unit's digit- 3, 13, 23, 33, 43, and ten numbers with 3 as the ten's digit - 30, 31, 32, 33, 34, 35, 36, 37, 38, 39.
So, required number = 5 + 10 = 15.
Answer:B | B |
deepmind/aqua_rat | Maths-Algebra | Farm Tax is levied on the 60% of the cultivated Land. The tax department collected total $ 3840 through the farm Tax from the village of Mr. willam. Mr. willam paid only $ 500 as farm tax. The percentage of total land of Mr. willam over the total taxable land of the village is : | [
"A)15.502%",
"B)25.7014%",
"C)12.502%",
"D)21.7014%",
"E)none"
] | Only trick n this question is to ignore 60% information as farm tax is levied uniformly in the village and that includes Mr William's land.
What percentage of tax Mr William paid ? This will be equal to the percentage of total cultivated land he holds over the total cultivated land in the village. That leads to (500/3840)x100 =13.02083%in percentage terms.
But the question asks ratio between his total land to total cultivated land. Hence the answer is 13.02083%x (100/60) = 21.7014% and the answer is not there in the options.
The correct answer is (D). | D |
deepmind/aqua_rat | Maths-Algebra | If John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 1 year would be | [
"A)(1.5)^4",
"B)4(1.5)",
"C)(1.05)",
"D)1 + (0.05)^4",
"E)1 + 4(0.05)"
] | f John invested $ 1 at 5 percent interest compounded annually, the total value of the investment, in dollars, at the end of 1 year would be
1(1.05)^1
1.05^1
C. (1.05) | C |
deepmind/aqua_rat | Maths-Algebra | x, y, and z are positive integers. The average (arithmetic mean) of x, y, and z is 11. If z is two greater than x, which of the following must be true?
I. x is even
II. y is odd
III. z is odd | [
"A)I only",
"B)II only",
"C)III only",
"D)I and II only",
"E)I and III only"
] | Given that:
x+y+z = 33 and z=x+2
using both equations
2x(Even) + y = 31 (Odd)
Since the sum is Odd 'y' has to be odd. Hence , only options (B) and (D) to be verified.
To check for 'x'.
x+y+z=33
x+z= 33- Odd
x+z= Even
Even + Even = Even
Odd+Odd = Even
ANSWER:B | B |
deepmind/aqua_rat | Maths-Algebra | If you write down all the numbers from 1 to 100, then how many times do you write 1 ? | [
"A)A)11",
"B)B)18",
"C)C)20",
"D)D)21",
"E)E)22"
] | Explanation:
Explanation:
Clearly, from 1 to 100, there are ten numbers with 1 as the unit's digit- 1, 11, 21, 31, 41, 51, 61, 71, 81, 91; and ten numbers with 1 as the ten's digit - 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 100
So, required number = 10 + 11 = 21.
Answer: D | D |
deepmind/aqua_rat | Maths-Algebra | If the two-digit integers A and B are positive and have the same digits, but in reverse order, which of the following could be the sum of A and B? | [
"A)41",
"B)42",
"C)43",
"D)44",
"E)45"
] | A two-digit number "cd" can be expressed algebraically as 10c+d.
The sum of A + B = (10c+d)+(10d+c)=11(c+d).
The only answer that is a multiple of 11 is 44.
The answer is D. | D |
deepmind/aqua_rat | Maths-Algebra | Of the three-digit integers greater than 800, how many have two digits that are equal to each other and the remaining digit different from the other two? | [
"A) 90",
"B) 82",
"C) 80",
"D) 45",
"E) 36"
] | Let the three digit number be represented as X Y Z.
There are 3 cases:
Case I.[ X=Y ]Z is not equal to XY :XXZorYYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 1 way
After XY are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(1)
[example numbers: 774,779,882,993 etc]
Case II.[ X=Z ]Y is not equal to XZ:XYXorZYZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Z can be chosen in 1 way
After XZ are chosen, Z can be chosen in 9 ways
Thus, possible No of digits = (3 ways) * (9 ways) * (1 way) = 27 ....(2)
[example numbers: 747,797,828,939 etc]
Case III.[ Y =Z ]X is not equal to YZ :XYYorXZZ
X can be either 7, 8 or 9, so digit at X can be chosen in 3 ways
After X is chosen, Y can be chosen in 9 ways
After Y is chosen, Z can have 1 way
Thus, possible No of digits = (3 ways) * (1 way) * (9 ways) = 27 ....(3)
[example numbers: 744,799,822,933 etc]
Therefore, total numbers of possible digits [sum of Case (1), (2)(3) above] = 27 + 27 + 27 - 1 = 80
One digit is subtracted from total number of possible digits to eliminate one possibility of XYZ = 700 to satisfy the condition that digit > 800.
Answer:(B) | B |
deepmind/aqua_rat | Maths-Algebra | The measurement of a rectangular box with lid is 25cmx18cmx18cm. Find the volume of the largest sphere that can be inscribed in the box (in terms of Οcm3). (Hint: The lowest measure of rectangular box represents the diameter of the largest sphere) | [
"A)288",
"B)48",
"C)72",
"D)972",
"E)964"
] | d=18, r=9;
Volume of the largest sphere= 4/3Οr3
= 4/3 *Ο*9*9*9= 972Οcm3 ANSWER:D | D |
deepmind/aqua_rat | Maths-Algebra | The current of a stream at 1 kmph. A motor boat goes 35 km upstream and back to the starting point in 12 hours. The speed of the motor boat in still water is? | [
"A)6",
"B)9",
"C)4",
"D)5",
"E)2"
] | S = 1
M = x
DS = x + 1
US = x - 1
35/(x + 1) + 35/(x - 1) = 12
x = 6
Answer: A | A |
deepmind/aqua_rat | Maths-Algebra | The present ages of three persons are in the proportion of 4 : 7 : 9. Eight years ago, the sum of their ages was 36. Find their present ages. | [
"A)20,35,45",
"B)8,20,28",
"C)16,28,36",
"D)12,21,27",
"E)None of these"
] | Let the present ages of three persons be 4K,7K and 9K respectively.
(4K - 8) + (7K - 8) + (9K - 8) = 36
20K = 60
K = 3
Therefore, then present ages are 12,21,27.
ANSWER:D | D |
deepmind/aqua_rat | Maths-Algebra | A certain board game is played by rolling a pair of fair six-sided dice and then moving one's piece forward the number of spaces indicated by the sum showing on the dice. A player is frozen if her opponent's piece comes to rest in the space already occupied by her piece. If player A is about to roll and is currently ten spaces behind player B, what is the probability that player B will be frozen after player A rolls? | [
"A)1/12",
"B)5/36",
"C)1/6",
"D)1/3",
"E)17/36"
] | no. of possible outcomes = 6*6 = 36
no. of outcomes that result a total of 10 (as A is 10 spaces behind B) = 3 ( (4,6), (5,5), (6,4) )
So, the probability = 3/36 =1/12(Option A) | A |
deepmind/aqua_rat | Maths-Algebra | The average mark of the students of a class in a particular exam is 70. If 5 students whose average mark in that exam is 50 are excluded, the average mark of the remaining will be 90. Find the number of students who wrote the exam? | [
"A)20",
"B)15",
"C)10",
"D)12",
"E)25"
] | Let the number of students who wrote the exam be x.
Total marks of students = 70 x.
Total marks of (x - 5) students = 90(x - 5)
70x - (5 * 50) = 90(x - 5)
200 = 20x => x = 10
Answer: C | C |
deepmind/aqua_rat | Maths-Algebra | A railway half ticket costs half the full fare and the reservation charge is the same on half ticket as on full ticket. One reserved first class ticket from Chennai to Trivandrum costs Rs. 216 and one full and one half reserved first class tickets cost Rs. 327. What is the basic first class full fare and what is the reservation charge? | [
"A)Rs. 105 and Rs. 6",
"B)Rs. 216 and Rs. 12",
"C)Rs. 210 and Rs. 12",
"D)Rs. 210 and Rs. 6",
"E)None"
] | Explanatory Answers
Let half of the full basic fare be Rs. X.
Therefore, full basic fare is Rs. 2X.
Let the reservation charge be Rs. Y per ticket.
Now, one full reservation ticket would cost 2X (basic fare) + Y (reservation charge)
2X + Y = 216 --- (1)
The total basic fare for one half and one full ticket = X + 2X = 3X and the total reservation charge is 2Y.
Hence, 3X + 2Y = 327 --- (2)
Solving (1) and (2) we get,
X = 105 and Y = 6
Hence, the full basic fare is 2X = Rs. 210 and the reservation charge is Y = Rs. 6
Answer D | D |
deepmind/aqua_rat | Maths-Algebra | The sale price of an article including the sales tax is Rs. 616. The rate of sales tax is 10%. If the shopkeeper has made a profit of 12%, then the cost price of the article is: | [
"A)280",
"B)579",
"C)500",
"D)400",
"E)100"
] | C
110% of S.P. = 616
S.P. = (616 * 100)/110 = Rs. 560
C.P = (110 * 560)/112 = Rs. 500 | C |
deepmind/aqua_rat | Maths-Algebra | Find the fourth proportional to 2.9, 4.6 and 7.6? | [
"A)12.05",
"B)13.5",
"C)15.23",
"D)15.34",
"E)16"
] | Formula = Fourth propotional = (b Γβ c)/a
A = 2.9, B = 4.6 and C = 7.6
(4.6 Γβ 7.6)/2.9 = 12.05
A | A |
deepmind/aqua_rat | Maths-Algebra | Given the equation e = f/4 + g/4^2 + h/4^3, where f, g, and h are each equal to 1 or 0, then e could be any of the values below EXCEPT: | [
"A)1/16",
"B)10/32",
"C)1/8",
"D)17/64",
"E)1/64"
] | e =f/4 + g/4^2 + h/4^3,
= f/4 + g/16 + h/64,
= (16f + 4g + h ) /64
Depending on whether f, g and h take 0 or 1:
substitute 0 or 1 for the different values of f, g and h.
Answer C | C |
deepmind/aqua_rat | Maths-Algebra | A & B THROW A DICE ALTERNATIVELY TILL ONE OF THEM GETS A '6' AND WINS THE GAME. WHAT WILL BE A PROBABILITY? | [
"A)4/11",
"B)5/11",
"C)6/11",
"D)7/11",
"E)8/11"
] | Whoever starts first will have a probability of 6/11 and the other has a probability of 5/11. So, if A starts, as has to be logically inferred from the question, pbbl that A wins = 6/11 and that B wins = 5/11.
Pbbl that the starting person wins = (1/6) + (5/6)*(5/6)*(1/6) + (5/6)*(5/6)*(5/6)*(5/6)*(1/6) + ... = G.P. with first term (1/6) and common ratio (5/6)*(5/6) = (1/6)/[1-(5/6)*(5/6)] = 6/11
ANSWER:C | C |
deepmind/aqua_rat | Maths-Algebra | 60% of the registered candidates in an election are from congress and 40% of the registered candidates are from BJP. If 3/4th of the registered Congress candidates and 1/5 of the registered BJP candidates fight election. What is the percentage of people fighting elections? | [
"A)34%",
"B)43%",
"C)53%",
"D)54%",
"E)56%"
] | Let total people be x
Congress =60/100*x=3x/5
3/4 of 3x/5=9x/20
Bjp=40/100*x=2x/5
1/5 of 2x/5=2x/25
Adding both
9x/20+2x/25=53x/100
Ans=53%
ANSWER:C | C |
deepmind/aqua_rat | Maths-Algebra | If 20 men can build a water fountain 56 metres long in 42 days, what length of a similar water fountain can be built by 35 men in 3 days? | [
"A)3 m",
"B)4 m",
"C)7 m",
"D)9 m",
"E)10 m"
] | Explanation :
Let the required length be x metres
More men, More length built (Direct Proportion)
Less days, Less length built (Direct Proportion)
Men 20: 35
Days 42: 3 : : 56 : x
Therefore (20 x 42 x x)=(35 x 3 x 56)
x=(35 x 3 x 56)/840=7
Hence, the required length is 7 m.
Answer : C | C |
deepmind/aqua_rat | Maths-Algebra | In a certain deck of cards, each card has a positive integer written on it, in a multiplication game a child draws a card and multiplies the integer on the card with the next large integer. If the each possible product is between 10 and 400, then the least and greatest integer on the card would be | [
"A)3 and 15",
"B)3 and 20",
"C)4 and 13",
"D)4 and 14",
"E)5 and 14"
] | Given: 10<x(x+1)<400.
Now, it's better to test the answer choices here rather than to solve:
If x=3 then x(x+1)=12>10 --> so, the least value is 3. Test for the largest value: if x=20 then
x(x+1)=20*21=420>400
Answer: B. | B |
deepmind/aqua_rat | Maths-Algebra | If you have 6 black socks, 4 blue socks, 8 brown socks, and 2 red socks in your sock drawer, what is the minimum number of socks that you need to pull out in the dark to be sure you had a matching pair? | [
"A)5",
"B)7",
"C)8",
"D)9",
"E)2"
] | A
5
At least 5, so that at least one color has two socks! | A |
deepmind/aqua_rat | Maths-Algebra | The difference between a number and its two-fifth is 510. What is 10% of that number ? | [
"A)33",
"B)85",
"C)37",
"D)27",
"E)28"
] | Explanation:
Let the number be x. Then, .
10 % 0f 850 = 85.
Answer: B) 85 | B |
deepmind/aqua_rat | Maths-Algebra | 40 percent of the ducks included in a certain side effects study were male. If some of the ducks had side effects during the study and 25 percent of the ducks who had side effects were male, what was the ratio of the side effect rate for the male ducks to the side effect rate for the female ducks? | [
"A)1/4",
"B)9/14",
"C)1/2",
"D)7/8",
"E)8/7"
] | Say total male = 40
Total female =60
Required ratio =( .25/40)/ (.75/60) = 1/2 C is the answer | C |
deepmind/aqua_rat | Maths-Algebra | This topic is locked. If you want to discuss this question please re-post it in the respective forum.
Matt and Peter can do together a piece of work in 20 days. After they have worked together for 12 days Matt stops and Peter completes the remaining work in 9 days. In how many days Peter complete the work separately. | [
"A)26 days",
"B)27.5 days",
"C)22.5 days",
"D)25.35 days",
"E)24 days"
] | Together they complete the job in 20 days means they complete 12/20 of the job after 12 days.
Peter completes the remaining (8/20) of the job in 9 days which means that the whole job(1) can be completed in X days.
<=> 8/20->9 <=> X=9/(8/20)=22.5Thus the answer is C. | C |
deepmind/aqua_rat | Maths-Algebra | N be a number,the 2,3 and 5 base notations u get last digit is 1.and two out of three the leading digit is 1. N is equal to | [
"A)31",
"B)63",
"C)74",
"D)91",
"E)98"
] | number shuld be in format of 2k+1,3k+1,5k+1
so take lcm of 2 3 5 we get 30k+1
so it may be 31 or 91
but in case of 31 leading digit of all 3 case is one
31 base2 = 11111
31 base3 = 1011
31 base5 = 111
so ans is 91
ANSWER:D | D |
deepmind/aqua_rat | Maths-Algebra | Vid intended to type a seven-digit number, but the two 3's he meant to type did not appear. What appeared instead was the five-digit number 52115. How many different seven-digit numbers could Vid have meant to type? | [
"A)10",
"B)16",
"C)21",
"D)24",
"E)27"
] | Vid intended to type a seven-digit number Should be 21.
there are two possibilities for placing 2 3s .
case 1: two 3s were missed consecutively. i.e. he typed 33 and it came blank on screen.
-5-2-1-1-5- in this arrangement we can fit 33 in 6 ways . (Six dashes, each dash represent one possible place for placing 33)
case 2: two 3s are not together, i.e. they have one or more digits between them .
-5-2-1-1-5- , in this arrangement
if we place first 3 at first dash i.e. 35-2-1-1-5- then the other 3 can fit into 5 places.
if we place first 3 at second dash i.e. -532-1-1-5- then the other 3 can fit into 4 places.
if we place first 3 at third dash i.e. -5-231-1-5- then the other 3 can fit into 3 places.
if we place first 3 at fourth dash i.e. -5-2-131-5- then the other 3 can fit into 2 places.
if we place first 3 at Fifth dash i.e. -5-2-1-135- then the other 3 can fit into 1 place.
so total 15 ways.
case 2 + case 1 = 6+ 15 = 21 ways
Answer C | C |
deepmind/aqua_rat | Maths-Algebra | A merchant has 100 lbs of sugar, part of which he sells at 7% profit and the rest at 12% profit. He gains 10 % on the whole. Find how much is sold at 7% profit? | [
"A)70 lbs",
"B)40 lbs",
"C)30 lbs",
"D)50 lbs",
"E)60 lbs"
] | These types ofweighted averagequestions can be solved in a variety of ways, so you can choose whichever method you find easiest/fastest. Here's another variation on the Weighted Average Formula:
A = # of pounds sold at 7% profit
B = # of pounds sold at 12% profit
A+B = 100 pounds
(.07A + .12B)/(A+B) = .10
.07A + .12B = .1A + .1B
.02B = .03A
2B = 3A
2/3 = A/B
So, for every 6 pounds of A, we have 4 pounds of B.
With 100 pounds total, we have 40 pounds of A and 60 pounds of B.
Option B | B |
deepmind/aqua_rat | Maths-Algebra | Express 22 mps in kmph? | [
"A)79.2 kmph",
"B)89.2 kmph",
"C)79.6 kmph",
"D)99.2 kmph",
"E)69.2 kmph"
] | 22 * 18/5 = 79.2 kmph
ANSWER:A | A |
deepmind/aqua_rat | Maths-Algebra | A number is said to be a βdigifacβ if each of its digits is a factor of the number itself. What is the sum V of the missing digits of the following five-digit digifac: 9, 5, 3 _ _ ? | [
"A) 5",
"B) 7",
"C) 9",
"D) 10",
"E) 14"
] | Here, the term βdigifacβ should look intimidating. You probably havenβt studied digifacs before, so how should you approach this problem? Well, keep in mind that digifacs arenβt being tested; in fact, the author of this question just made that term up, and then defined it for you. What makes this question hard is that the non-challenge-seeker (I think I just made that term up, tooβ¦) will see the unfamiliar term βdigifacβ and lose faith immediately. βI donβt know what that is!β She who finds the challenge in the GMAT fun, however, will read the definition and think βgot it β I need to find the two digits that ensure that 9, 5, and 3 are both factors of the overall number, and that the remaining two digits are also factorsβ. And work from there. The number must be divisible by 5, so the only units digits that work are 0 or 5. And the number must be divisible by 9 (and also 3), so we need the sum V of all digits to be a multiple of 9. 9 + 5 + 3 = 17, so our only options are to get the sum to 18 (by adding 1) or to 27 (by adding 10). A quick glance at the answer choices shows that 0 1 isnβt an option. Why not? That would require 0 to be one of the digitsβ¦and 0 isnβt a factor of anything. So the units digit must be 5, making the tens digit 5, and we have 95,355. That number is a multiple of 5, 3, and 9, so it works:the correct answer is D, and more importantly this fun challenge required no βtrivialβ information about digifacsβ¦that term only existed to obscure the link between the given information and the path to the answer.D | D |
deepmind/aqua_rat | Maths-Algebra | What percent of 9.6 kg is 28 gms ? | [
"A)25",
"B)66",
"C)288",
"D)29",
"E)17"
] | Explanation:
Required percentage = (28/9600 * 100)% = 29/100% = 0.29%
Answer: D) .29% | D |
deepmind/aqua_rat | Maths-Algebra | the cost of manufacturing a popular model car is made up of three items:cost of raw material,labour and overheads- in a year the cost of three items were in the ration of 4:3:2.next year the cost of the raw material rose by 10% ,labour cost increased by 8% but overhead reduced by 5%.then %increase int the price of the car ? | [
"A)7.67%",
"B)6%",
"C)0.54%",
"D)9.54%",
"E)8.54%"
] | before increase total cost = 4+3+2=9,
after increasing the cost = 9.54
so increase of .54 over 9 , equal to 6%
ANSWER:B | B |
deepmind/aqua_rat | Maths-Algebra | Average expenditure of a person for the first 3 days of a week is Rs. 350 and for the next 4 days is Rs. 420. Average expenditure of the man for the whole week is: | [
"A)350",
"B)370",
"C)390",
"D)430",
"E)None"
] | Explanation:
Assumed mean = Rs. 350
Total excess than assumed mean = 4 Γ (Rs. 420 - Rs. 350) = Rs. 280
Therefore, Increase in average expenditure = Rs. 280/7 = Rs. 40
Therefore, Average expenditure for 7 days = Rs. 350 + Rs. 40 = Rs. 390
Correct Option: C | C |
deepmind/aqua_rat | Maths-Algebra | If a rectangular billboard has an area of 130 square feet and a perimeter of 46 feet, what is the length of each of the longer sides? | [
"A)4",
"B)7",
"C)8",
"D)13",
"E)26"
] | This question can be solved algebraically or by TESTing THE ANSWERS.
We're told that a rectangle has an area of 130 and a perimeter of 46. We're asked for the length of one of the LONGER sides of the rectangle.
Since the answers are all INTEGERS, and the area is 130, the shorter side will almost certainly be closer to 10 (since 10x10 = 100, but we're NOT dealing with a square). Answer B (7) does NOT divide evenly into 130,
IF...
The shorter side = 10...
The area = 130/10 = 13 = the longer side
Perimeter = 10+10+13+13 = 46
D | D |
deepmind/aqua_rat | Maths-Algebra | A standard Veggiematik machine can chop 35 carrots in 5 minutes. How many carrots can 3 standard Veggiematik machines chop in 3 minutes? | [
"A)63",
"B)87",
"C)90",
"D)98",
"E)112"
] | Direct Relationship:-
1 standard Veggiematik machine - 35 Carrots - 5 minutes,
1 standard Veggiematik machine - 7 Carrots - 1 minute,
Now
3 standard Veggiematik machine - ? Carrots - 3 minutes,
Hence = 7X3X3 =63 Carrots
Answer A | A |
deepmind/aqua_rat | Maths-Algebra | The toll for crossing a certain bridge is $0.75 each crossing. Drivers who frequently use the bridge may instead purchase a sticker each month for $12.00 and then pay only $0.30 each crossing during that month. If a particular driver will cross the bridge twice on each of x days next month and will not cross the bridge on any other day, what is the least value of x for which this driver can save money by using the sticker? | [
"A)14",
"B)15",
"C)16",
"D)28",
"E)29"
] | Option #1: $0.75/crossing....Cross twice a day = $1.5/day
Option #2: $0.30/crossing....Cross twice a day = $0.6/day + $13 one time charge.
If we go down the list of possible answers, you can quickly see that 14 days will not be worth purchasing the sticker. 1.5x14 (21) is cheaper than 0.6x14 +13 (21.4)...it's pretty close so let's see if one more day will make it worth it... If we raise the number of days to 15, the sticker option looks like a better deal...1.5x15 (22.5) vs 0.6x15 + 13 (22). Answer: A | A |
deepmind/aqua_rat | Maths-Algebra | A train running at the speed of 60 km/hr crosses a pole in 9 sec. What is the length of the train? | [
"A)296 m",
"B)267 m",
"C)297 m",
"D)150 m",
"E)255 m"
] | Speed = 60 * 5/18 = 50/3 m/sec
Length of the train = speed * time = 50/3 * 9
= 150 m
Answer:D | D |
deepmind/aqua_rat | Maths-Algebra | In how many ways can 4 men & 3 women can be made from a gang of 7 men & 8 women ? | [
"A)91",
"B)94",
"C)89",
"D)10",
"E)19"
] | Explanation:
7C4 * 8C3 = 91
A | A |
deepmind/aqua_rat | Maths-Algebra | Patrick has three daughters named Avery, Bridget, & Catherine. He decides he wants to make a 3-letter password using the a combination of the each of their first initials (e.g. ABC, CBA, etc.). How many different permutations can he come up with? | [
"A)3",
"B)5",
"C)6",
"D)8",
"E)11"
] | Permutation calc is: n P r = n! / (n-r)! 3 P 3 = 3!/(3-3)! = 3x2x1/0!=6/1=6 Correct answer is C (6) ANSWER:C | C |
deepmind/aqua_rat | Maths-Algebra | At exactly what time past 8:00 will the minute and hour hands of an accurate working clock be precisely perpendicular to each other for the first time? | [
"A)20 13/21 minutes past 8:00",
"B)20 13/17 minutes past 7:00",
"C)21 3/23 minutes past 7:00",
"D)21 9/11 minutes past 7:00",
"E)22 4/9 minutes past 7:00"
] | A1 = hour angle
A2 = minute angle
A1-A2 = 90
Assume the minutes = M
A1 = (8*60+M)/12*60 )*360
A2 = M*360/60
Solving all three equation , results in the answer A | A |
deepmind/aqua_rat | Maths-Algebra | What is the 26th digit to the right of the decimal point in the decimal form of 6/11? | [
"A)3",
"B)4",
"C)5",
"D)6",
"E)7"
] | 6/11 = 0.54545454...
The even numbered positions in the decimal expansion are all 4.
The answer is B. | B |
deepmind/aqua_rat | Maths-Algebra | The weight of every type A widget is the same, the weight of every type B widget is the same, and the weight of every type C widget is the same. If the weight of 7 type A widgets is equal to the weight of 3 type B widgets, and the weight of 5 type B widgets is equal to the weight of 7 type C widgets. What is the ratio of the total weight of 1 type A widget and 1 type B widget, to the total weight of 1 type B widget and 1 type C widget? | [
"A)1:2",
"B)2:3",
"C)3:4",
"D)4:5",
"E)5:6"
] | 5B = 7C and so B = 7C/5
7A = 3B and so A = 3B/7 = 3C/5
A+B = 3C/5 + 7C/5 = 10C/5
B+C = 7C/5 + C = 12C/5
The ratio of A+B:B+C = 10:12 = 5:6
The answer is E. | E |
deepmind/aqua_rat | Maths-Algebra | If x is divisible by 2, 7, and 11, which of the following must also be a divisor of x? | [
"A)308",
"B)154",
"C)70",
"D)44",
"E)21"
] | If Multiple divisors of any integers are mentioned just take the LCM of all the divisors and the integer will be divisible by that.
LCM of 2,7,11= 154
Hence x must be divisible by 154
Hence B | B |
deepmind/aqua_rat | Maths-Algebra | A hollow iron pipe is 21 cm long and its external diameter is 8 cm. If the thickness of the pipe is 1 cm and iron weighs , then the weight of the pipe is | [
"A)3.496 kg",
"B)3.696 kg",
"C)3.690 kg",
"D)9.696 kg",
"E)3.296 kg"
] | Explanation:
External radius = 4 cm,
Internal radius = 3 cm.
Volume of iron = =
Weight of iron = (462 x 8)gm = 3696 gm = 3.696 kg
Answer: B) 3.696 kg | B |
deepmind/aqua_rat | Maths-Algebra | In how many ways can 21 books on English and 19 books on Hindi be placed in a row on a
shelf so that two books on Hindi may not be together? | [
"A)1240",
"B)1280",
"C)1340",
"D)1440",
"E)1540"
] | In order that two books on Hindi are never together, we must place all these books as under:
X E X E X E X .... X E X
where E - denotes the position of an English book and X that of a Hindi book.
Since there are 21 books on English, the number of places marked X are therefore, 22. Now, 19 places out of 22 can be chosen in
22C19 = 22C3 = 22 x 21 x 20 = 1540 ways.
3 x 2 x 1
Hence, the required number of ways = 1540.
ANSWER:E | E |
deepmind/aqua_rat | Maths-Algebra | A is half good a work man as B and together they finish a job in 14 days. In how many days working alone B finish the job? | [
"A)98 days",
"B)21 days",
"C)17 days",
"D)18 days",
"E)19 days"
] | WC = 1:2
2x + x = 1/14 => x = 1/42
2x = 1/21 => 21 days
Answer:B | B |
deepmind/aqua_rat | Maths-Algebra | Jack invested $2000 in fund A and $2000 in fund B. Over the next two years, the money in Fund A earned a total interest of 12 percent for the two years combined and the money in fund B earned 30 percent annual interest compounded annually. Two years after Jack made these investments. Jack's investment in fund B was worth how much more than his investment in fund A? | [
"A)1. $1000",
"B)2. $1500",
"C)3. $900",
"D)4. $1140",
"E)5. $700"
] | interest on fund A will be 240. rate of interest will be 6% per annum simple interest as 12% is for 2 year. this will make investment A 2240 at the end of 2nd year.
interest on fund B will be 1380 on 30% interest compounded annually. This will make investment B 3380 at the end of 2nd year.
Difference in investment B and investment A=3380-1690=1140
answer is D. | D |
deepmind/aqua_rat | Maths-Algebra | The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. Find out the average age of the team. | [
"A)23 years",
"B)20 years",
"C)24 years",
"D)21 years",
"E)25 years"
] | Explanation:
Number of members in the team = 11
Let the average age of of the team = xx
=> Sum of the ages of all 11 members = 11x11x
Age of the captain = 26
Age of the wicket keeper = 26 + 3 = 29
Sum of the ages of 9 members of the team excluding captain and wicket keeper
=11xβ26β29=11xβ55=11xβ26β29=11xβ55
Average age of 9 members of the team excluding captain and wicket keeper
=11xβ559=11xβ559
Given that 11xβ559=(xβ1)11xβ559=(xβ1)
β11xβ55=9(xβ1)
β11xβ55=9xβ9β2x=46
βx=462=23 years
ANSWER IS A | A |
deepmind/aqua_rat | Maths-Algebra | A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work in : | [
"A)8",
"B)9",
"C)4",
"D)18",
"E)None"
] | Ratio of rates of working of A and B = 2 : 1
So, ratio of times taken = 1 : 2
B's 1 day's work = 1/12
Therefore A's 1 day's work = 1/6
(A + B)'s 1 day's work = (1/6 + 1/12)= 1/4
So, A and B together can finish the work in 4 days.
Answer: C | C |
deepmind/aqua_rat | Maths-Algebra | The edge of a cube is 2a cm. Find its surface? | [
"A)24a8",
"B)24a4",
"C)24a1",
"D)24a2",
"E)24a7"
] | 6a2 = 6 * 2a * 2a = 24a2
Answer:D | D |
deepmind/aqua_rat | Maths-Algebra | If 20% of a number is equal to one-third of another number, what is the ratio of first number to the second number? | [
"A)2:5",
"B)1:4",
"C)5:3",
"D)6:11",
"E)2:3"
] | Let 20% of A = 1/3 B
then 20A/100 = 1B/3
A/5 = B/3
A/B = 5/3
A:B = 5:3
Answer is C | C |
deepmind/aqua_rat | Maths-Algebra | if (HE)^H=SHE,where the alphabets takes the values from (0-9) & all the alphabets are single digit then find the value of (S+H+E) | [
"A)10",
"B)13",
"C)5",
"D)19",
"E)data in sufficient"
] | 25^2=625
6+2+5=13
ANSWER:B | B |
deepmind/aqua_rat | Maths-Algebra | Find the simple interest on Rs.580 for 11 months at 9 paisa per month? | [
"A)574",
"B)270",
"C)566",
"D)266",
"E)121"
] | I = (580*11*9)/100 = 574
Answer: A | A |
deepmind/aqua_rat | Maths-Algebra | In how many ways can a cricket eleven be chosen out of a batch of 15 players. | [
"A)1254",
"B)1365",
"C)1204",
"D)5421",
"E)1234"
] | Required number of ways
= 15C 11 = 15C (15-11)
= 15 C 4
15C4 = 15 * 14 * 13 * 12 / 4 * 3 * 2 *1
= 1365
Ans: B | B |
deepmind/aqua_rat | Maths-Algebra | x^2 + bx + 72 = 0 has two distinct integer roots; how many values are possible for b? | [
"A)3",
"B)6",
"C)8",
"D)12",
"E)24"
] | As 72 is positive either both roots are + or -
but as 'b' is +ve, both the roots carry same sign, i.e. +ve, and the factors are as below
72, 1
2, 36
4, 18
8, 9
24, 3
6, 12
ANSWER:D | D |
deepmind/aqua_rat | Maths-Algebra | A car covers a distance of 624 km in 6 Β½ hours. Find its speed? | [
"A)104 kmph",
"B)194 kmph",
"C)109 kmph",
"D)174 kmph",
"E)101 kmph"
] | 624/6
=104 kmph
Answer:A | A |
deepmind/aqua_rat | Maths-Algebra | Two varieties of steel, A and B, have a ratio of iron to chromium as 5:1 and 7:2, respectively. Steel C is produced by mixing alloys A and B at a ratio of 3:2. What is the ratio of iron to chromium in C? | [
"A)17 : 73",
"B)78 : 14",
"C)45 : 30",
"D)73 : 17",
"E)4 : 9"
] | In 6 parts of alloy A, 5 parts are iron, and 1 part is chromium.
In 9 parts of alloy B, 7 parts are iron and 2 parts are chromium.
First, to compare the two alloys, get the same number of parts in total - we can use 18. So we have:
In 18 parts of alloy A, 15 parts are iron and 3 are chromium.
In 18 parts of alloy B, 14 parts are iron and 4 are chromium.
So combining 3 of A with 2 of B, we'd be combining 45 and 28 parts of iron, or 73 parts of iron, with 9 and 8 of chromium, or 17 of chromium, so 73 to 17 is the answer.
ANSWER:D | D |
deepmind/aqua_rat | Maths-Algebra | A shipment of 7 television sets contains 2 black-and-white sets and 6 color sets. If 2 television sets are to be chosen at random from this shipment, what is the probability that at least 1 of the 2 sets chosen will be a black-and-white set? | [
"A)1/7",
"B)1/4",
"C)6/21",
"D)11/28",
"E)13/28"
] | I get 6/21, which is not in the answer choices.
the probability of getting at least one b/w TV is 1-(the probability of getting 2 color TVs)
1-C(6,2)/C(7/2)=6/21
C | C |
deepmind/aqua_rat | Maths-Algebra | If x, y, and z are positive integers and 2x = 4y = 5z, then the least possible value of x + y + z is | [
"A)40",
"B)50",
"C)55",
"D)60",
"E)19"
] | given 2x=4y=5z
x+y+z in terms of x
= x+(2x/4)+(2x/5) = 38x/20=19x/10
now checking with each of the answers and see which value gives a minimum integer value.
A x = 10/19*40 , not an integer
B,C,E can be ruled out similarly.
D is minimum value as x = 19*10/19 = 10
Answer is E | E |
deepmind/aqua_rat | Maths-Algebra | 10^(65) ΓΒ· 10^(64) = ? | [
"A)1",
"B)10",
"C)100",
"D)1000",
"E)10000"
] | 10^(65) ΓΒ· 10^(64) = 10^ (65-64) = 10^1
= 10
Answer : B | B |
deepmind/aqua_rat | Maths-Algebra | If 4XZ + YW = 7 and XW + YZ = 14, what is the value of the expression (2X + Y)(2Z + W)? | [
"A)9.",
"B)12.",
"C)35.",
"D)16.",
"E)18."
] | (2x+y)*(2z+w) = 7+2(14) =35
Answer : C | C |
deepmind/aqua_rat | Maths-Algebra | A and B invest 3,000 and 4,000 in a business. A receives 10 per month out of the profit as a remuneration for running the business and the rest of profit is divided in proportion to the investments. If in a year βAβ totally receives 390, what does B receive? | [
"A)375",
"B)360",
"C)350",
"D)260",
"E)None of these"
] | In a year, for A, total amount as a remuneration
= 10 Γ 12 = 120
β΄ Amount of Aβs profit = 390 β 120 = 270
Ratio of investment = 3 : 4
Let total profit = x
Then, Bβs profit = (x β 270)
β΄ 3/3+4Γx=270β x = 630
β΄ Bβs profit = 630 β 270 = 360
Answer B | B |
deepmind/aqua_rat | Maths-Algebra | Find the rate at Simple interest, at which a sum becomes four times of itself in 15 years. | [
"A)10%",
"B)20%",
"C)30%",
"D)40%",
"E)50%"
] | Explanation:
Let sum be x and rate be r%
then, (x*r*15)/100 = 3x [important to note here is that simple interest will be 3x not 4x, beause 3x+x = 4x]
=> r = 20%
Option B | B |
deepmind/aqua_rat | Maths-Algebra | Find a a prime number from the options below. | [
"A)37",
"B)38",
"C)39",
"D)40",
"E)42"
] | Clearly, 37 is a prime number.
A | A |
deepmind/aqua_rat | Maths-Algebra | $ 3650 is divided among 4 engineers, 3 MBAs and 5 CAs such that 3 CAs get as much as 2 MBAs and 3 Engs as much as 2 CAs .Find the share of an MBA. | [
"A)400",
"B)150",
"C)250",
"D)450",
"E)350"
] | 4E+3M+5C=3650
3C=2M, that is M=1.5C
3E=2C that is E=.66 C
Then, (4*0.66C)+(3*1.5C)+5C=3650
C=3650/12.166
C=300
M=1.5C
=450.
ANSWER : D 450 | D |
deepmind/aqua_rat | Maths-Algebra | The present population of a town is 4032. Population increase rate is 20% p.a. Find the population of town before 2 years? | [
"A)2500",
"B)2800",
"C)3500",
"D)3600",
"E)2050"
] | P = 4032
R = 20%
Required population of town = P/(1 + R/100)^T
= 4032/(1 + 20/100)^2
= 4032/(6/5)^2
= 2800(approximately)
Answer is B | B |
deepmind/aqua_rat | Maths-Algebra | If X is the sum of first 50 positive even integers and Y is the sum of first 50 positive odd integers, what is the value of x-y? | [
"A)0",
"B)25",
"C)50",
"D)75",
"E)100"
] | First even minus first odd = 2-1 = 1;
The sum of first 2 even integers minus the sum of first 2 odd integers = (2+4)-(1+3) = 2;
The sum of first 3 even integers minus the sum of first 3 odd integers = (2+4+6)-(1+3+5) = 3;
...
We can see the patterns here, so the sum of first 50 positive even integers minus the sum of first 50 positive odd integers will be 50.
Answer: C. | C |
deepmind/aqua_rat | Maths-Algebra | The difference between the simple interest received from two different sources on Rs.1600 for 3 years is Rs.13.50. The difference between their rates of interest is | [
"A)0.1%",
"B)0.28%",
"C)0.35%",
"D)0.42%",
"E)0.5%"
] | (1600xR1x3)/100-(100xR2x3)/100 =13.50
4800(R1-R2)=1350
R1-R2 = 1350/4800=0.28%
answer : B | B |
deepmind/aqua_rat | Maths-Algebra | A cricket bat is sold for $900, making a profit of $75. The profit percentage would be | [
"A)9%",
"B)12%",
"C)10%",
"D)36%",
"E)40%"
] | 75/(900 - 75) = 75/825 = 0.9 bit more than 9%.
Answer: A | A |
deepmind/aqua_rat | Maths-Algebra | A train running at 25 km/hr takes 20 seconds to pass a platform. Next, it takes 12 seconds to pass a man walking at 5 km/hr in the same direction. Find the length of the train and that of the platform. | [
"A)a) 200/3m175/3m",
"B)b) 90m70m",
"C)c) 50m45m",
"D)d) 100/3 m200/3",
"E)e) none of these"
] | Hi Math gurus correct me if I am wrong. I wondered i reached the answer mentioned here i.e 100m and 25m
lets solve it
To find out length of train the train, which is must cover the static point of the man as well as the distance covered the man during 12 sec.
The man covered the distance during 12sec is 5*5/20*12=15m so the train covered a distance in 12 sec= 25*5/20*12=75
so the length of the train(Lt) is 15+75=90m
Now crossing the platform means length of train+length of platform(Lt+p)= 20*25*5/20=125m Now the length of platform (Lp) is= 125-90=35m
So answer is 90m and 35m Must beBeven though its mentioned 90m and 70m thinking so typo mistake........... | B |
deepmind/aqua_rat | Maths-Algebra | 3x^2 + 5x - 2 = | [
"A)(3x-1)(x+2)",
"B)(3x-4)(x+2)",
"C)(3x-4)(x-2)",
"D)(3x-2)(x+4)",
"E)none of above"
] | 3x^2 + 5x - 2
= 3x^2 + 6x - x - 2
= 3x (x + 2) - (x+2)
= (3x-1) (x+2)
Option A | A |
deepmind/aqua_rat | Maths-Algebra | A farmer spent $33 on feed for chickens and goats. He spent 40% money on chicken feed, which he bought at a 20% discount off the full price, and spent the rest on goat feed, which he bought at full price. If the farmer had paid full price for both the chicken feed and the goat feed, what amount would he have spent on the chicken feed and goat feed combined? | [
"A)$36.30",
"B)$38.50",
"C)$39.20",
"D)$39.50",
"E)$40.60"
] | A farmer spent 40% money on chicken feed, so he spent 0.4*$33=$13.2 on chicken feed, thus he spent the remaining 33-13.2=$19.8 on goat feed.
Now, since he bought chicken feed at a 20% discount then the original price of it was x*0.8=$13.2 --> x=$16.5.
Therefore if the farmer had paid full price for both the chicken feed and the goat feed, then he would he have spent 16.5+19.8=$36.3.
Answer: A | A |
deepmind/aqua_rat | Maths-Algebra | The G.C.D. of 1.08, 0.36 and 0.9 is: | [
"A)0.03",
"B)0.9",
"C)G.C.D.=0.18",
"D)0.2",
"E)0.21"
] | Given numbers are 1.08, 0.36 and 0.90.
H.C.F. of 108, 36 and 90 is 18,
H.C.F. of given numbers = 0.18.
Answer: Option C | C |
deepmind/aqua_rat | Maths-Algebra | In a renowned city, the average birth rate is 7 people every two seconds and the death rate is 3 people every two seconds. Estimate the size of the population net increase that occurs in one day. | [
"A) 172,700",
"B) 172,800",
"C) 172,900",
"D) 173,000",
"E) 173,100"
] | This question can be modified so that the birth rate is given every m seconds and the death rate is given every n seconds.
For this particular question : Increase in the population every 2 seconds = 7-3 = 4 people.
Total 2 second interval in a day = 24*60*60/2 = 43,200
Population increase = 43,200 * 4 = 172,800. Hence B. | B |
deepmind/aqua_rat | Maths-Algebra | Mr Yadav spends 60% of his monthly salary on consumable items and 50% of the remaining on clothes and transport. He saves the remaining amount. If his savings at the end of the year were 19008, how much amount per month would he have spent on clothes and transport? | [
"A)4038",
"B)8076",
"C)9691.2",
"D)1584",
"E)1625"
] | β΅ Amount, he have spent in 1 month on clothes transport = Amount spent on saving per month
β΅ Amount, spent on clothes and transport
= 19008β12 = 1584
Answer D | D |
deepmind/aqua_rat | Maths-Algebra | A company produces 72000 bottles of water everyday. If a case can hold 9 bottles of water .How many cases are required by the company to hold its one day production | [
"A)2000",
"B)4500",
"C)5000",
"D)8000",
"E)9000"
] | Number of bottles that can be held in a case = 9.
Number of cases required to hold 72000 bottles = 72000/9=8000 cases.
So the answer is D =8000 | D |
deepmind/aqua_rat | Maths-Algebra | The expression 10^14β130 is divisible by all of the following integers EXCEPT | [
"A)9",
"B)2",
"C)4",
"D)8",
"E)11"
] | Yeah. I agree this question has two answers which are (B) and (E). If 10 is power to odd number and equal or more than 5, then the answer choice (A) is correct. | A |
deepmind/aqua_rat | Maths-Algebra | If 3 pounds of dried apricots that cost x dollars per pound are mixed with 2 pounds of prunes that cost y dollars per pound, what is the cost, in dollars, per pound of the mixture? | [
"A)(3x + 2y)/5",
"B)(3x + 2y)/(x + y)",
"C)(3x + 2y)/(xy)",
"D)5(3x + 2y)",
"E)3x + 2y"
] | Total Cost = Weight(in pounds) * Price/pound;
To find Total cost/pound, Divide by total pounds.
Cost of Dried apricots = 3x;
Cost of prunes = 2y;
Cost per pound = (3x + 2y)/5;
Ans is (A). | A |
deepmind/aqua_rat | Maths-Algebra | A garrison of 400 men had a provision for 31 days. After 20 days 180 persons re-enforcement leave the garrison. Find the number of days for which the remaining ration will be sufficient? | [
"A)65 days",
"B)45 days",
"C)20 days",
"D)16 days",
"E)18 days"
] | 400 --- 31
400 --- 11
220 --- ?
400*11 = 220*x => x =20 days.
Answer: C | C |
deepmind/aqua_rat | Maths-Algebra | Cara and Dan race around a running track. Cara runs at a constant rate of one lap every 4 minutes and Dan runs at a constant rate of one lap every 5 minutes. If they both start at the same time, how many minutes will it take for Cara to get exactly one lap ahead of Dan? | [
"A)18",
"B)20",
"C)22",
"D)24",
"E)25"
] | Let x be the number of minutes it takes for Cara to get one lap ahead.
Then Cara ran x/4 laps and Dan ran x/5 laps.
x/4 = 1+x/5
5x=20+4x
x=20
The answer is B. | B |
deepmind/aqua_rat | Maths-Algebra | How many three digits odd numbers can be formed by using the digits 4,5,6,7,8,9 if the repetition of the digits not allowed? | [
"A)60",
"B)50",
"C)40",
"D)70",
"E)30"
] | For a number to be odd the unit place must be filled by the number 5,7 or 9 in 3 ways. Since the repetition of digits not allowed the ten's and hundred's place can be filled in by 5 and 4 ways respectively. So the required number of numbers =3*5*4 = 60. Answer : A | A |
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